It was karna who tried to defeat arjun when they returned after completing their education from Drona in gurukul
EKLAVYA, the son of a tribal chief defeated Arjuna in an archery contest.
Drona, the guru of the Pandava princes refused to teach archery to Eklavya because Eklavya a was tribal. Eklavya, however was very resourceful. After he returned to the jungle he made a statue of Drona and with single minded concentration and determination practised archery daily in the presence of this statue. Soon he became a very skilful archer. Once, Drona and Arjuna alongwith the other Pandava princes went hunting and they chanced upon Eklavya honing his archery skills. Drona was very impressed with Eklavya especially when he learnt how Eklavya had taught himself archery. However, the Pandava princes especially Arjuna became very jealous. An archery contest in which Eklavya had to compete with the Pandava princes was held. Eklavya emerged the victor, even defeating Arjuna the expert archer and Drona's best student.
Drona, was naturally upset because Eklavya had defeated his favourite student Arjuna. So, Drona in the guise of demanding "guru dakshin" ( a student's free will offering to his master after completion of his training by the guru) demanded the thumb of Eklavya's right hand. Eklavya, the humble and obedient student immediately chopped off the thumb of his right hand and offered it to Drona. Consequently, Eklavya could never again shoot an arrow and Arjuna continued to be the best archer.